We want to compare the growth of more than two time series. So is it worth to estimate on absolute number or shall i convert the series in to index number.
Your question is not understandable for me. Please explain more and make it clear.
Sachin: Growth rate calculation is invariant to the measurement unit. So, it does not matter. For example, (20-10)/10 = 1= (20,000-10,000)/10,000.
A strange question and a strange example in Francis' answer. An index is formed by dividing all absolute values by a certain value (mostly by the value of one period or an average). Such an operation has, of course, no effect on the percentage changes, these are the same for absolute values and for the index.
If by growth you mean absolute differences (e.g. changes of private consumption compared to changes of income both measured in some currency), because you think that there is a linear relation between these variables, it is better to relate these differences instead of the differences or their indices.
depends on which point of view you're willing to calculate it. You should consider the metrics and the time period you're working on. As an example let's consider daily price evolution in a year ( we want to see the growth rate per month) we should consider getting the price on the first day of the given month then subtract it from the last price at the end of the month divided by the price at the first day of the month for the annual you consider the price first day in the year and the price at the end of the year ( the you use the same formula) for pourcentage you just multiply by 100
The percentage changes are independent from the measurement of a variable, i.e. they are the same for the absolute values and for any index of them. By the way, the discussion shows, that the calculation of percentages is not well taught in school. We were taught, that the percentage difference p from X to Y is:
p=(Y-X)/X*100. In fact, p=(Y-X)/X=Y/X-1, which is simply a rational number (maybe rounded) or a rational approximation for a real number. One can write p in many different formats: e.g. 0.25 = 250/1000 = 1/4 =250000 p.p.m. = 25% = 250%o etc. I think there are infinite possibilities. That % is merely a format of writing a number can be seen in EXCEL: If e.g. in a cell there is the number 2.435 (typed in or as a result of an operation) and one chooses "%" as a format for numbers, one gets 243.50%.
Sachin More
Calculating growth rate from 2 to 6 uses h= Log base 10 ((Xt/Xt-1) /difference 6-2) . Antilog(h) minus 1 then multiply by 100. This gives for example growth rate per year from 2 to 6.
Calculating just overall growth rate (Xt/Xt-1)*100
Chuck, your calculation of the geometric mean growth (more general: change, because a variable could decrease, too) seems to be unnecessarily complicated. Normal calculators include an nth-root button. Therefore, one need not go via logs (can be any base) and delog, but for the average change between e.g. X0 and X6 one can calculate the 6th root of X6/X0 and subtract 1, then you get the rate of change. If the result is e.g. 0.0371 (for 280 and 225 as X6 and X0), this can be read as 3.71%. For your overall growth (change) rate you foregot to deduct 1. One should not multiply by 100 (see may former answer). If in EXCEL 225 is in A1 and 280 is in A7, one can simply write "=(a7/a1)^(1/6)" and choose the number format "%" with 2 decimals and one should get 3.71%.
Apart from that, all these calculations arrive at the same results for absolute values and for indices. Therefore, there is no necessity to calculate indices (unless there are other reasons to do that).
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